Answer:
x < -4
Step-by-step explanation:
-3x > 12
----- ----
-3 -3
12 ÷ -3 = -4
Which means:
x < -4
(The sign changes because the equation is divided by a negative number)
Hope this helped.
Answer:
x <-4
Step-by-step explanation:
-3x > 12
Divide each side by -3. remembering to flip the inequality
-3x/-3 > 12/-3
x <-4
A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.
Answer:
48, 6
Step-by-step explanation:
The ratio of the pieces is 6 to 1
Add them together to get the total
6+1 = 7
Divide the total length by 7
56/7 = 8
Multiply the ratios by 8
6*8 = 48
1*8 = 6
The peices are 48 and 6
Rate of change or rate of change
A farmer has 80 feet of wire mesh to surround a rectangular pen.
A) Express the area A of the pen as a function of x, also draw the figure of A indicating the admissible values of x for this problem.
B) What are the dimensions of the maximum area pen?
Answer:
Step-by-step explanation:
A). Let the dimensions of the rectangular pen are,
Length = l
Width = x
Since, farmer has the wire measuring 80 feet to surround the the pen.
Perimeter of the pen = 80 feet
2(l + x) = 80
l + x = 40
l = 40 - x ------(1)
Area of the rectangular pen = Length × width
= lx
By substituting the value of l from equation (1),
Area (A) of the pen will be modeled by the expression,
A = (40 - x)
A = 40x - x²
B). For maximum area of the pen,
Derivative of the area = 0
[tex]\frac{d}{dx}(A)=0[/tex]
[tex]\frac{d}{dx}(A)=\frac{d}{dx}(40x-x^2)[/tex]
= 40 - 2x
And (40 - 2x) = 0
x = 20
Therefore, width of the pen = 20 feet
And length of the pen = 40 - 20
= 20 feet
Dimensions of the pen should be 20 feet by 20 feet.
When a fridge is imported, a customs value of 10% must be paid for its value. If the value of the fridge after paying the customs value is rs. 55,000/-. What is the value before paying customs duty?
Answer:
55000×100/90
61,111.111
Which expression is equivalent to 9+y+y+3
Answer:
b
Step-by-step explanation:
You only need to add the real numbers and the ys.
Answer:
12 + 2y
Step-by-step explanation:
9+y+y+3
Combine like terms
9+3 + y+y
12 + 2y
Ethan buys a video game on sale. If the video game usually costs $60, and it was on sale for 20% off, how much did Ethan pay? Round to the nearest whole dollar.
Ethan will pay $31.99 with the discount.
How? This is the answer because:
If 39.99 is 100%, and you are trying to find 20%...
1. you need to set it up as a ratio (of course, you do not need to do this, but it is easier for me to do it this way)
2. the ratio will look like this: 39.99/100% x/20%
3. all we need to do from here is to cross multiply!
4 39.99 x
---------- = ----------
100 20
-price is on the top and percent on the bottom
-you would now do 39.99 times 20
-then divide by 100
5. once you have 20% of 39.99, you need to subtract that answer from the total
6. 39.99 - 7.998 = 31.992 (you need to round to the nearest hundredth)
Hope this helps <3
Complete the sentence that explains why Write an Equation is a reasonable strategy for solving this problem. Because the answer may be _________ the numbers in the problem.
Answer:
4 e
Step-by-step explanation:
dz6dxrx xrrx6 xz33x4xr4x xrx
Riley wants to make 100ml of 25% saline but only has access to 12% and 38% saline mixtures. x= 12% y=38%
Answer:
x = 50
y = 50
Step-by-step explanation:
[tex]\begin{bmatrix}x+y=100\\ 0.12x+0.38y=25\end{bmatrix}[/tex]
.12(100-y) + .38y = 25
x = 50
y = 50
Solve 8x + c = k for x
Answer:
x = 1/8(k-c)
Step-by-step explanation:
8x + c = k
Subtract c from each side
8x +c-c = k-c
8x = k-c
Divide each side by 8
8x/8 = (k-c)/8
x = 1/8(k-c)
Answer:
x-1/8(k-c)
Step-by-step explanation:
A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 47 states. What is the probability that she selects the route of three specific capitals?
Answer:
1 / 97290
Step-by-step explanation:
The number of ways of selecting 3 specific route capitals from 47 states can be obtained thus :
Probability = required outcome / Total possible outcomes
Total possible outcomes = 47P3
Recall :
nPr = n! / (n-r)!
47P3 = 47! / (47-3)! = 47! / 44! = 97290
Hence, probability of selecting route if 3 specific capitals is = 1 / 97290
Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) 102.53070, (b) 656.980, (c) 0.008543210, (d) 0.000257870, (e) -0.0357202
Answer:
Kindly check explanation
Step-by-step explanation:
Rounding each number to 4 significant figures and expressing in standard notation :
(a) 102.53070,
Since the number starts with a non-zero, the 4 digits are counted from the left ;
102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2
(b) 656.980,
Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.
656.980 = 657.0 (4 significant figures) = 6.57 * 10^2
(c) 0.008543210,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3
(d) 0.000257870,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4
(e) -0.0357202,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2
How do I figure this question out
Answer:
Orthocenter would be in the middle of the shape.
Step-by-step explanation:
B.
Lost-time accidents occur in a company at a mean rate of 0.8 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2
Answer:
0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.
Step-by-step explanation:
We have the mean during the interval, which means that the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Lost-time accidents occur in a company at a mean rate of 0.8 per day.
This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.
10 days:
This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]
What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]
[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]
[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]
So
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]
0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.
4 people take 3 hours to paint a fence assume that all people paint at the same rate How long would it take one of these people to paint the same fence?
Answer:
12
Step-by-step explanation:
A graph of 2 functions is shown below. graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2 Which of the following is a solution for f(x) = g(x)? (2 points) x = −2 x = 1 x = 0 x = −1
9514 1404 393
Answer:
(b) x = 1
Step-by-step explanation:
A graph shows the solution to f(x) = g(x) is x = 1.
__
We want to solve ...
g(x) -f(x) = 0
x^3 +2x^2 -x -2 -(-11/3x +11/3) = 0
x^2(x +2) -1(x +2) +11/3(x -1) = 0 . . . . . factor first terms by grouping
(x^2 -1)(x +2) +11/3(x -1) = 0 . . . . . . the difference of squares can be factored
(x -1)(x +1)(x +2) +(x -1)(11/3) = 0 . . . . we see (x-1) is a common factor
(x -1)(x^2 +3x +2 +11/3) = 0
The zero product rule tells us this will be true when x-1 = 0, or x = 1.
__
The discriminant of the quadratic factor is ...
b^2 -4ac = 3^2 -4(1)(17/3) = 9 -68/3 = -41/3
This is less than zero, so any other solutions are complex.
Zoe has 4 pounds of strawberries to make pies. How many ounces of strawberries Is this?
64 oz.
60 oz.
68 oz.
72 oz.
Work Shown:
1 pound = 16 ounces
4*(1 pound) = 4*(16 ounces)
4 pounds = 64 ounces
The population, P(t), in millions, of a country, in year t, is given by the formula P(t) = 24 + 0.4t. What are the values of the population for t = 10, 20,
and 30?
Answer:
B. 28, 32, 36 millions
Step-by-step explanation:
Given:
P(t) = 24 + 0.4t
Where,
P(t) = population in millions
t = number of years
✔️Value of the population when t = 10:
Plug in t = 10 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(10)
P(t) = 24 + 4
P(t) = 28 million
✔️Value of the population when t = 20:
Plug in t = 20 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(20)
P(t) = 24 + 8
P(t) = 32 million
✔️Value of the population when t = 30:
Plug in t = 30 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(30)
P(t) = 24 + 12
P(t) = 36 million
I need help ASAP please no links
Answer: D' = (1, -1)
Step-by-step explanation:
When dilating by a 1/2 you take a point and divide the x and y of the point in half. So D before is (2,-2) and then divide that by a 1/2, which gives us our answer (1, -1).
PLS
Write the equation of the piecewise function that is represented by its graph.
IS IT A, B, C, OR D
9514 1404 393
Answer:
a) domain bounds are -1 ≤ x ≤ 1, x > 1
Step-by-step explanation:
In considering the definition of any piecewise function, the domain descriptions in the function definition must match the pieces shown in the graph.
Here, the right segment has no upper bound, so x > 1 is an appropriate description of its domain.
The left segment has the points at x=-1 and x=1 included, so the appropriate domain description for that is -1 ≤ x ≤ 1.
The one answer choice that combines these domain descriptions is ...
[tex]\displaystyle f(x)=\begin{cases}x^2,&\text{if }-\!1\le x\le1\\\sqrt{x},&\text{if }x>1\end{cases}[/tex]
Reasoning by induction
Question 1 options:
1)
develops a general conclusion based on observations of cases.
2)
develops a general conclusion based on given information.
3)
starts with assumptions that are known to be valid to draw another new truths.
4)
uses patterns to create logical proofs.
Answer:
1because the occasion of cases
Please helppppppppp!!!!
Terminal point for 4π/3
(cos4π/3 ,sin4π/3)
{cos(π+π/3) ,sin(π+π/3)}= (-cosπ/3 ,-sinπ/3)
or ,(- 1/2, -√3/2)
OPTION C
Describe the system of equations
How many solutions does this system have.
Answer:
Step-by-step explanation:
One solution, at the point of intersection, (3,3)
Simplify
x * x^5 / x^2 * x
Hari earns Rs 4300 per month. He spends 80% from his income. How much amount does he save in a year?
Answer:
Hari saves $ 10,320 in a year.
Step-by-step explanation:
Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:
100 - 80 = 20
4300 x 0.20 x 12 = X
860 x 12 = X
10320 = X
Therefore, Hari saves $ 10,320 in a year.
Find the sum of the geometric series given a1=−2, r=2, and n=8.
A. -510
B. -489
C. -478
D. 2
Answer:
A. -510
Step-by-step explanation:
We are given the variable values:
a = -2r = 2n = 8Geometric series formula:
[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]
Plugging in values we have:
[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]
Simplifying the equation we are left with:
[tex] \frac{ - 2(255)}{1} = - 510[/tex]
If 4 gallons of gasoline cost $13.76, how much will 11 gallons of gasoline cost?
Answer:
x=37.84
Step-by-step explanation:
We can write a ratio to solve
4 gallons 11 gallons
--------------- = ----------------
13.76 x dollars
Using cross products
4x = 11*13.76
4x=151.36
Divide by 4
4x/4 = 151.36/4
x=37.84
Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).
Answer:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope
1) Determine the slope
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-2, 6) and (3,-2):
[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]
Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
2) Plug in a point [tex](x_1,y_1)[/tex]
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
I hope this helps!
If (-3)^-5 = 1/x, what is the value of x?
Answer:
-243
Step-by-step explanation:
(-3) (-3) (-3) (-3) (-3) = - 243
[tex]\frac{1}{-243 }[/tex]
You wish to create a 5 digit number from all digits; 0 1 2 3 4 5 6 7 8 9
Repetition is not allowed
* 0 cannot be first as it does not count as a place value if it is first. Ie. 027 is a 2 digit number
How many even numbers can you have?
Answer:
10234
Step-by-step explanation:
one is the smallest number so its first
and then you can place zero
after that just place the second smallest number
and so on
The triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answer:
x=12
Step-by-step explanation:
each side of the smaller triangle, we can multiply by 4 to get the side of the larger triangle
ex: 8*4=32 and 17*4=68
so we can assume that 15*4= 4x+12
60=4x+12
48=4x
x=12
Answer:
x = 12
Step-by-step explanation:
The triangles are similar so we can use ratios
4x+12 32
------- = ------------
15 8
Using cross products
(4x+12) *8 = 15 * 32
(4x+12) *8 = 480
Divide each side by 8
(4x+12) *8/8 = 480/8
4x+12 = 60
Subtract 12 from each side
4x+12 -12 = 60-12
4x = 48
Divide by 4
4x/4 = 48/4
x = 12
A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 98% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 1.1. The study found that for a sample of 1027 teenagers the mean number of energy drinks consumed per week is 5.9. Construct the desired confidence interval. Round your answers to one decimal place.
Answer:
The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{1.1}{\sqrt{1027}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 5.9 - 0.1 = 5.8 drinks per week.
The upper end of the interval is the sample mean added to M. So it is 5.9 + 0.1 = 6 drinks per week.
The 98% confidence interval for the mean number of energy drinks consumed per week by teenagers is (5.8, 6).
